Interaction potentials used in particle simulations are typically written as a sum of terms which depend on just a few relative particle positions. Traditional simulation methods move all particles at each time step, and may thus spend a lot of time updating interparticle forces. In this Letter we introduce adaptively restrained particle simulations (ARPS) to speed up particle simulations by adaptively switching on and off positional degrees of freedom, while letting momenta evolve. We illustrate ARPS on several numerical experiments, including (a) a collision cascade example that demonstrates how ARPS make it possible to smoothly trade between precision and speed and (b) a polymer-in-solvent study that shows how one may efficiently determine static equilibrium properties with ARPS.